 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2017/1/a/i/solution

(x_{n})

(X, d)

\forall ε > 0 \exists N \forall m, n \geq N : d (x_{m}, x_{n}) < ε .

The index

N

may depend on

ε

, but must work for every pair of sufficiently late terms. No candidate limit is part of this definition.

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